Two former Labour home secretaries, a security minister and a former "independent" reviewer of terror laws have called for the swift review of the communications data bill, following the Woolwich killing. If I didn't believe these were the first reactions to a shocking crime, I'd put the interventions of Jack Straw, Lord (John) Reid, Lord (Alan) West and Lord (Alex) Carlile down to cynical opportunism, because I'm afraid that is very much how it looked.

Give our guys the tools to fight terror on the streets, they say; "the proportionate tools", eagerly adds the former reviewer of terror laws, Lord Carlile. But not one of them bothered to produce the smallest evidence that the type of surveillance proposed in the "snoopers' charter" would have stopped the two suspects, Michael Adebolajo and Michael Adebowale.

The simple flaw in their case is that both men were already known to MI5, which was aware of their associations and radicalisation. The agency, it's claimed, may even have tried to recruit Adebolajo. If intelligence officers had thought it necessary, they possessed all the powers they needed to monitor the pair's emails, texts, phone calls and internet use. Some 500,000 intercepts are already granted every year. So the idea that giving police and MI5 untrammelled access to the nation's communications data would have provided vital information that would have averted Lee Rigby's murder is almost certainly wrong.

Lone-wolf attacks in a free society are notoriously difficult to anticipate. Evidence may emerge that MI5 overlooked some important clues, but an inability to intercept the pair's communications was clearly not the critical factor. Yet here were the ministers and Carlile, implying that it was. In all their pronouncements, I did not hear one of them admit that monitoring of terror suspects is a matter of routine for MI5 and the agency has all the tools it required for this case, except precognition.

It was all very reminiscent of Labour's years, when these ministers pushed for more and more oppressive legislation to control and monitor the average citizen, on the grounds that massive surveillance and coercion were the only answers to Islamist terror. Remember the costly ID card fiasco, stop and search, stringent control order regimes – for those who had not been found guilty of a crime – and 90 day detention without charge?

By contrast, David Cameron produced a fairly balanced reaction, condemning the murders, making calls for unity and rightly applauding the self-possessed heroism of Ingrid Loyau-Kennett, who distracted one of the suspects. No new powers announced, no clampdown on the rights of British citizens to conduct their lives without fear of the state scooping up the who, when, what and where of all their communications.

People have questioned the need for the prime minister's dash back from France and the Cobra meeting, saying it seemed a bit panicky, but in one way the response was refreshing. Nick Clegg and communities minister, Eric Pickles, both argued that the communications data bill, which Clegg successfully blocked from the Queen's speech, could not have prevented the Woolwich murder.

But the forces advocating oppressive laws are never far from the surface. At the Home Office, there are still several senior civil servants, most notably Charles Farr, head of security and counterterrorism, who are committed to mass surveillance. Not just out of the belief that the public would be safer, one suspects, but because their personalities incline them to authoritarian solutions – obedience and control over personal freedom.

It's an area of policy where leftwingers can become very right wing, and the right wing can exhibit remarkably enlightened views. The divide is often more psychological than ideological, though it's true that many authoritarian members of Labour governments, such as John Reid, often started out on the far left. Incidentally, what Reid did not feel it necessary to disclose during his interview on Newsnight last week is that he is paid handsomely by the security industry firm G4S.

Last year's scrutiny of the draft communications data bill by a joint committee of MPs and peers identified the problems of the system of mass surveillance that Reid favours. The first and crucial point, apart from the universal intrusion entailed, is that it does not necessarily lead you to the right individuals. There is too much information to process, clunky algorithms throw up false positives, and there are always means of communication that intelligence officers are going to miss. The two alleged killers didn't need the internet or mobile phones to plan and carry out an attack that was no different to an ambush in the dark ages, and the idea that a sophisticated surveillance system can prevent such archaic savagery is simple-minded.

Ah, say the enthusiasts, this system is not merely about predicting the attack. It would sift emails, texts, interactions on social networking sites to pick up the first stirrings of radicalisation and then allow constant monitoring of suspects as they evolve to more dangerous states of mind. Even if it were true that such a system could prevent another Woolwich, the apparatus that en masse fingers people's apparent beliefs, draws conclusions about what is inside their minds and seemingly predicts intention is impossible to accommodate in a free society. This is for the very obvious reasons that it will get things wrong and gives too much power to the government of the day.

I don't want to repeat the arguments against the communications data bill because it is dormant, at least for this parliament, but it is worth mentioning that one of the parliamentary committee's chief worries was the level of access that the "snoopers' charter" was likely to give to, among others, town halls, health and safety inspectors, NHS trusts, the Environment Agency and even the Charity Commission. The system that allows MI5 and police access to people's communications data through a trap door in phone companies and internet providers would soon be made available to every inquisitive jobsworth in the country.

Sooner or later, another surveillance bill will appear, probably devised by Charles Farr, and almost certainly supported by Reid and his nervy, authoritarian pals. If interceptions are to be upgraded to meet the challenges of developing communications, we have to be sure that they are compliant with a fully functioning democracy.

In response to this terrible event, the government didn't do too badly and we should be thankful that, for the moment, we are not facing another Labour attack on our freedom.